Political Altruism of Transboundary Water Sharing

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University of Wyoming
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Economics and Finance Faculty Publications Economics and Finance
2008
Political Altruism of Transboundary Water Sharing
A. Bhaduri
Edward B. Barbier
University of Wyoming, [email protected]
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Publication Information
Bhaduri, A. and Barbier, Edward B. (2008). "Political Altruism of Transboundary Water Sharing."B E Journal of Economic Analysis &
Policy8.1.
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Political Altruism of Transboundary Water
∗
Sharing
AnikBhaduriandEdwardB.Barbier
Abstract
Inthepaper,usingapoliticalaltruismmodel,wemakeanattempttoexplainwhyanupstream
country might agree to a treaty that recognizes and enforces the water claims of a downstream
country. Inanaturalextensionofthestandardeconomicmodel,itispossibletoexplaintheabove
phenomena,byallowingforaltruismbetweencountries. Thealtruisticconcernsofthecountries
are dependent on other country’s willingness to have a good political relationship. If both the
countries maintain favorable political relations with one another, then the upstream country will
care about the impacts of its water diversion on the downstream country’s welfare. The paper
alsoillustratesthecaseofwatersharingoftheGangesRiverbetweenIndiaandBangladesh. The
GangesRiver,likemanyotherriversintheworld,ignorespoliticalboundaries.InBangladesh,the
finaldownstreamcountryalongtheGanges,freshwateravailabilitydependsontheshareofwater
divertedbytheupstreamcountry,India. Fordecades,IndiaandBangladeshfailedtoresolvethe
water-sharingissuesoftheGangesRiver. However,in1996,bothIndiaandBangladeshsigneda
majornewagreementonwatersharing(GangesRiverTreaty)inanefforttoresolvethedispute.
Usingthepoliticalaltruismmodeldevelopedinthepaper,weexaminewhydespiteneedingmore
water than is available under the treaty, India has adapted to shortages instead of resorting to
conflictwithBangladesh.
KEYWORDS:transboundary,watersharing,politicalaltruism
∗Thepaperstemsfromtheproject“EconomicAnalysisofUpstream-DownstreamWaterAlloca-
tioninDevelopingCountries,”fundedbyStanfordUniversityandtheHewlettFoundation. Weare
grateful to Ken Arrow and Larry Goulder for their support and guidance, as well as participants
ataworkshopatStanfordfortheirhelpfulcommentsonanearlierversionofthepaper. Wealso
express our thanks to Thomas Crocker, Rob Godby, Charles Mason and Larry Weatherford for
providingvaluableandcriticalcomments,andMargieReisforherassistance.
Bhaduri and Barbier: Political Altruism of Transboundary Water Sharing
1. Introduction
With a growing population and rapidly expanding water demand for development,
especially for irrigated agriculture, an upstream country would clearly benefit
from continuing to divert more water in transboundary water sharing of a river.
From a standard economic perspective, it would be rational for the upstream
country not to care about the downstream country and put no weight whatsoever
on the net benefit of the latter. However, we know that many upstream countries
and many individuals in upstream countries do care about the welfare of
downstream countries. This is evident as countries sign far-reaching international
agreements on water sharing that seem to be against their own narrowly defined
economic self-interests (Wolf et al. 2003).
The issue to be addressed by this paper is the question of why upstream
countries agree to forego unilateral water diversion in order to cooperate with
downstream countries on water sharing. In agreeing to a treaty, why do the
upstream countries not obtain compensation from downstream countries in
exchange for lowering upstream diversion levels? The paper proposes that the
efficient allocation of water sharing between an upstream and a downstream
country may be the result of an alternative motivation: limited pure (non
paternalistic) altruism between countries.
In this paper, a pure altruistic model is presented in which the countries
care about each other with respect to water sharing. Political relations between the
countries are crucial elements influencing the altruistic behavior of the countries.
Here, a model is developed that closely follows the median voter model
(Hotelling1929; Black 1948; Downs 1957) to determine the political relationship
each country is willing to have with the other country. Given the determined
altruistic concerns of the countries, the political altruism model allows
determination of the optimal allocation of water sharing between two countries;
and demonstrates the conditions under which altruistic cooperation between
countries can guarantee an efficient water allocation.
Most of the altruism literature (Chiappori 1988; Bergstorm 1989; Yann
2001) is related to household behavior. This paper makes a unique attempt in
defining the altruism of countries on the basis of political democracy, and
represents a first analysis to explore transboundary water sharing in the
framework of political altruism.
The paper illustrates the case of water sharing of the Ganges River
between India and Bangladesh. In Bangladesh, the final downstream country
along the Ganges, freshwater availability depends on the share of water diverted
by the upstream country, India. For decades, India and Bangladesh failed to
resolve the water-sharing issues of the Ganges River. In 1996, both India and
Bangladesh signed a major new agreement on water sharing (Ganges River
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Treaty) in an effort to resolve the dispute. Using the political altruism model, we
examine why despite needing more water than is available under the treaty, India
has adapted to shortages instead of resorting to conflict with Bangladesh.
The paper is structured as follows. The next section outlines the political
altruism model of water sharing between the upstream and the downstream
country. The key feature of this model is the determination of the expected
political relationships in each country, which is necessary for the solution of the
model. Section 3 explains how the expected political relationships are derived.
Given these political relationships, section 4 shows the conditions that determine
the optimum allocation of water shared between the upstream and the downstream
country. Section 5 illustrates the Ganges case study, while section 6 discusses the
simulation techniques and results. Finally, the conclusion summarizes the main
findings and results of the paper.
2. The Water Sharing Model
Since 1948, about three hundred international water agreements have been signed
and negotiated (Wolfe et. al 2003); and most of them were resolved in
negotiations and treaties signed without provision of any side payments, or
compensations from downstream countries. It suggests that the upstream countries
do care about the welfare of the downstream countries at least to some extent. A
natural extension of the standard economic model makes it possible to explain the
above phenomena by allowing for political altruism between countries. In this
section, we address such issues by formulating a general pure altruistic model.
Previous work has indicated that altruism is common among countries, citing
unconditional aid from rich to poor countries as one example (Johansson et. al
2002). Here, we also allow for altruism but not through the conventional “aid
flow” mechanism.
In the following model, altruism is conditional and entails reciprocity.
This paper justifies the reciprocity in altruistic behavior by relating it to a political
relationship. If the upstream country expects that the downstream country is
willing to have a good political relationship, then the upstream country will be
altruistic and will allow more water to flow to the downstream nation. Similarly,
if the downstream country expects a good political relationship with the upstream
country, it will display altruistic concern and, settle for a lesser amount of water
flowing from upstream.
Kolm (2000) has shown that reciprocal behavior among individuals can
overcome a number of failures of exchange, thus improving efficiency and
economic productivity. Here we show that similar reciprocal altruism between
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Bhaduri and Barbier: Political Altruism of Transboundary Water Sharing
countries can also guarantee an efficient allocation of water if the altruistic
behavior is reflected in each country’s preferences.1
We attempt to capture the reciprocal altruism by constructing each
country’s net benefit in a framework of interdependent utility functions, which
depends on their own private benefit and weighted benefit of the other country2.
Suppose two countries A and B share freshwater of a river. Country A is an
upstream country and has an opportunity to unilaterally divert water, while
country B is a downstream country where the freshwater availability depends on
the water usage of the upstream country. Let wA denote the amount of water
diverted by upstream country and wB be the amount of water available to the
downstream country. If W is the deterministic flow of river water, then it follows
that wA +wB =W. 3 (1)
It is assumed that welfare in both countries is affected by this water
allocation decision. Water users in the upstream country will gain if wA increases;
similarly, a decline in wB will affect adversely water users in downstream country.
Let the benefit functions of each country be denoted as BA(wA) and BB(wB). We
make the standard assumption that both benefit functions are concave with respect
to their arguments.4
If the upstream country cares only about its own welfare, then it would
maximize its benefit function BA(wA) by choice of water diversion, wA, subject
only to W. The result is the welfare maximizing unilateral diversion of water by
the upstream country A.
A different outcome might occur, however, if the countries are concerned
about the implications of water allocation on the broader political and economic
relationships between the two countries. Consider a general model, where the net
benefit,NBi, of country i (i=A, B) , in the framework of a system of

1 Altruism between countries can exist independently of the political system. In a leviathan or a
bureaucratic political economy, for instance, altruism towards other countries exists, and is
dictated by one or few people. However in a democratic society altruistic behavior of a country is
based on the collective preference of the people reflected in electoral votes, and hence tends to be
more stable than determined in an autocratic or bureaucratic system (Goodin 2005 ).
2 Previous studies using interdependent utilities to model altruism include Becker (1974, 1981,
ch.8), Bergstrom (1989, 1999), Bruce and Waldman (1991), Dutta and Michel (1998), Hori (1992,
1997), Hori and Kanaya (1989), Horowitz and Wang (2001), Kimball (1987), Kolm (1969), Loury
(1981), Ray (1987), and Stark (1995).
3
We consider water flow to be deterministic to make the model analytically more tractable.
4 A social welfare function includes the welfare of citizens as well as firms. In the model
presented, the net benefits of the countries do not represent the total social surplus as the payoffs
to firms are not considered. The assumption is made for analytical simplification as inclusion of
firm’s payoff requires additional parameters and more complexities in simulation procedure.
Future work can model the total social surplus in the form of a net benefit as a function of both
citizen and firms, and create an attempt to address the wider issue of social welfare.
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interdependent utility functions, depends on their own private benefit,Bi, and a
weighted benefit of the other country, kiNBj (cid:11)j(cid:122)i(cid:12). The weights ki are the
altruistic concerns of country i for j, and are based on the degree (better or worse)
of the political relationship(cid:92)j that country i is expecting from country j. If
country i expects that country j is willing to have a good political relationship,
then country i will be more altruistic towards country j. Though the ruling
political party in each country decides the level of foreign relationship, it often
echoes by public opinion expressed in the form of political votes given to each
party’s political agenda. The electorate is assumed to have a notion or preference
over policies. Not knowing the true foreign policy of country j, country i forms an
expectation of the political relationship county j is willing to support,E((cid:92)i ),
based on the distribution function of desired policies of the electorate in country j.
The net benefit functions of the countries are assumed to be
NBA (cid:32)BA(wA )(cid:14)k NBB(wA,wB ) (2)
A
NBB (cid:32)BB(wB )(cid:14)k NBA(wA,wB ) (3)
B
where k (cid:32)E((cid:92)B );k (cid:32)E((cid:92)A ), and wA (cid:14)wB (cid:32)W
A B
Interdependent net benefit functions introduce an additional layer of
complexity. Interdependence engenders indeterminacy. If the net benefit of
country A depends on the net benefit of country B which in turn depends on the
net benefit of country A….; the net benefits of each country recursively depend on
each other. This kind of recursivity arises because agents recognize that the other
country’s net benefit depends on its own. Equations 2 and 3 can be re-expressed
1 (cid:62) (cid:64)
as NBA (cid:32) BA(wA)(cid:14)k BB(wB) (4)
A
1(cid:16)k k
A B
1 (cid:62) (cid:64)
NBB (cid:32) BB(wB)(cid:14)k BA(wA) (5)
B
1(cid:16)k k
B A
As a stability condition, we assume that each country values its own
marginal benefit from the consumption of water more than the marginal benefit of
the other country for the same amount of water consumption, implying k k (cid:31)1
A B
in equations 4 and 5.5 As the degrees of expected political relations E((cid:92)i ) are

5 Whenk k (cid:33)1, an awkward consequence occurs, as the net benefits are monotonically
A B
decreasing in their arguments. Both countries prefer less water to more and they disagree about the
allocation of water because each country wants the other country to take a larger proportion of
water. Bergstorm (1989) argues that stability provides an appropriate concept to solve the paradox.
Whenk k (cid:33)1, the solution is unstable and should not be considered as valid. But ifk k (cid:31)1,
A B A B
each country with independent preference would prefer more water than less and the solution will
be stable.
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Bhaduri and Barbier: Political Altruism of Transboundary Water Sharing
crucial elements influencing the altruistic behavior of the countriesk ; the next
i
section describes how these crucial expectation parameters can be derived.

3. Determination of Expected Political Relationships

The competing political parties of each country may differ in their views on
transboundary water, which will influence how each party views the common
objective of maximizing the welfare of the citizens. For instance, one party might
argue that cooperative efforts between countries in transboundary water sharing
can provide benefits that far exceed the gains from maximizing national welfare
only. A rival party, however, could hold the contradictory view and emphasize
maximizing only its own country’s welfare. The difference in political opinion
would yield an optimal transboundary water sharing policy through the electoral
competition process that differs from that devised by a single social planner. Here,
our objective is to explore how such a transboundary water policy consistent with
the collective choice of the people in the face of competing electoral parties might
arise. A key requirement is that this political consensus over the collective choice
of an optimal transboundary water policy is achieved through a democratic voting
system. A common method of characterizing such electoral behavior in social
choice theory is the median voter model6, which has been applied extensively to
problems of conflict resolution (Joan et al. 1999; Reynal 2001; Colomer 2002). In
such applications of the median voter model, in the event of a disagreement, each
rival party submits a policy offer and the median voter chooses one party whose
policy stands closest to the voter’s preference (Powell 2000). A similar
application of the median voter model to determine the expected political
relationship seems appropriate in the context of our model of water sharing
between countries.
In the standard median voter model, agents (voters and parties) make
decisions in one dimension, i.e. over a single political issue that is the source of
conflict among the competing parties. However, in most of the countries political
parties have different perspectives on a range of foreign and domestic policies.
Thus, one way that our model differs from the usual median voter model is that
we assume that the political parties make decisions in more than one dimension,
i.e. over a complete “set” or “agenda” of policies. However, the median voter
model does not apply easily to multi-dimensional voting models. Plott(1969)
suggests that in two-dimensional cases, a median voter exists only in cases where
voter tastes are very symmetrically distributed. We apply the median voter model

6 The median voter rule was formulated by Harold Hotelling as an application of a theorem in
economics (Hotelling 1929) and was developed further by Duncan Black (1948) and Anthony
Downs (1957).
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to the internal political decision process of both countries involved in the
transboundary water dispute. In both the upstream and downstream country the
electorate acts on its voting preferences, choosing one political agenda by electing
one of the two competing parties.
The following model formalizes the above ideas in a simple game
theoretic framework.
We consider the internal political process in country i (i=A, B). We
assume that in country i there are two political parties, the liberal party Xi and the
nationalistic party Yi.7 The political parties campaign for votes in a political
election; foreign policy, economic policy, and other non-economic domestic
policies are the key electoral issues.8 Each political party (k= X, Y) offers two
kinds of policies: a set of(cid:92)i domestic economic policy and foreign policies with
k
country j( j(cid:122)i); and, a set of(cid:73)i other domestic policies unrelated to the foreign
k
and economic policies. We assume that the foreign policy of a country proposed
by each party is associated with its proposed domestic economic policy.9
The offers (cid:92)i and (cid:92)i can be expressed in terms of an index of the
X Y
political parties’ degree of hostility to country j, with a value for (cid:92)i close to zero
k
implying a very “hostile” relationship with the other country j and very
“restrictive” economy while a value of (cid:92)i close to one implying a very “friendly”
relationship and very “liberalized” economy, then (cid:92)i and (cid:92)i can be expressed
X Y
as0(cid:31)(cid:92)i (cid:31)(cid:92)i (cid:31)1. Similarly,(cid:73)i can be expressed as an index of political parties
Y X k
concern over non-economic domestic policies, with a value close to one implying
high importance of non economic domestic policies while a value of (cid:73)i close to

7 Liberal refers to a party preferring more liberalized trade policies and good political relations.
Nationalistic refers to a party that promotes more restrictive trade policies and is not as concerned
with foreign political relations.
8 The political parties are assumed in the model to be myopic about the electorate’s preferred
political relationship. They are concerned only about making political “offers” that will help them
win votes in the next election only.
9 In the model, the degree to which domestic economic policy is associated with foreign policy is
a theoretical construct. Essentially, we are assuming that the upstream and downstream countries
are both small open economies, and thus the association of domestic economic policy with foreign
policy would naturally follow. For example, this association could be represented in terms of an
index of the political parties’ degree of hostility to economic relations with a foreign country, or
indeed to “globalization” generally, and it could be measured practically by openness to trade, e.g.
(Exports+Imports)/GDP. But we have ignored suggesting such an explicit measure as openness to
trade, because such a measure can also be influenced by factors other than the electorate‘s altruism
towards a foreign country.
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Bhaduri and Barbier: Political Altruism of Transboundary Water Sharing
zero implying low importance of such domestic policies. The restriction on (cid:73)ican
be expressed as0(cid:31)(cid:73)i (cid:31)(cid:73)i (cid:31)1.10
X Y
Before the election, the parties, Xi and Yi of country i announce their political
agenda if they come into power. The objective function of the political parties is
to win an election by choosing an equilibrium set of policies given the voter’s
preference of policies. The voter’s preference over the political relationship with
the other country and the desired non economic domestic policies are represented
byZ and Z respectively. We assume that Ziand Zi are uncorrelated.
1 2 1 2
In the median voter model, the chance of winning an election of a political
party is influenced by the decision rule of the median voter. The median voter is
the representative deciding voter in a compulsory voting procedure, and it chooses
the political agenda by voting for one of the two political parties. The median
voter’s preference of policies depends on the distribution function of voter’s
preference of policies.
We assume that the voter’s preferred policy, Z (l (cid:32)1,2) , is normally and
l
independently distributed with mean m and variance(cid:86)2.The political parties
l l
have no knowledge of Z , but they believe that Z is randomly distributed
l l
according to cumulative distribution f(Z ) with associated probability density
l
(cid:119)F(Z)
function f(Z )where (cid:32) f(Z) . As the political party’s action and objective of
l (cid:119)Z
winning an election are based on the belief of the voter’s distribution function, the
model is probabilistic in nature. In such a typical probabilistic model, the political
parties do not directly observe the idiosyncratic pattern of voter’s preference. The
variance of the distribution function provides a degree of information or
knowledge about such uncertainty of voter’s preferred policy in a given election.
Using the parity concept, we determine the median voter’s decision
criteria, which are as follows:
(cid:92) (cid:14)(cid:92)
Political party X is chosen ifZ (cid:16)(cid:92) (cid:33)(cid:92) (cid:16)Z , or if Z (cid:33) X Y (cid:32)(cid:92)ˆ .11
1 Y X 1 1 2
(cid:73) (cid:14)(cid:73)
Conversely, political party Y is chosen if Z (cid:16)(cid:73) (cid:33)(cid:73) (cid:16)Z or if Z (cid:33) X Y (cid:32)(cid:73)ˆ .
2 X Y 2 2 2

10 (cid:73) could also be considered a platform inclination or disposition as opposed to a specific policy.
11 Decision Rule: Political party X is preferred if the absolute distance between voter’s preferred
and the offered policy is less than the distance between the preference and political part Y’s
offered policy. This is true if (cid:92) (cid:33)(cid:92) , and (cid:92) (cid:33) Z ,(cid:92) (cid:31)Z or (cid:92) (cid:31)(cid:92) (cid:31)Z .
X Y X 1 Y 1 Y X 1
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The direct chance of winning the election (with a clear electoral mandate)
for the political parties X and Y will be P(Z (cid:33)(cid:92)ˆ ,Z (cid:31)(cid:73)ˆ ) and P(Z (cid:33)(cid:73)ˆ ,Z (cid:31)(cid:92)ˆ )
1 2 2 1
respectively.12
However, some times the electorate’s mandate is not reflected in the
results of an election. Such a situation may arise if the electorate prefers a
liberalized economy with a friendly foreign policy (Z (cid:33)(cid:92)ˆ ) and simultaneously
1
attaches high importance to the non-economic domestic policy (Z (cid:33)(cid:73)ˆ ). The
2
situation may also arise if the electorate chooses a restrictive economy with a
hostile foreign policy (Z (cid:31)(cid:92)ˆ ) and simultaneously gives low importance to the
1
other non-economic domestic policy (Z (cid:31)(cid:73)ˆ ). Such outcomes occur because the
2
competing parties have political agendas of more than one dimension. If the
electorate’s preference over the multi-dimensional policy offer is structured in
such a way, then it may elect either of the political parties. In such a situation, we
have13
P(Z (cid:33)(cid:92)ˆ ,Z (cid:33)(cid:73)ˆ )(cid:32)P(Z (cid:31)(cid:92)ˆ ,Z (cid:31)(cid:73)ˆ ). (6)
1 2 1 2
Given equation (6), the probability of each political party wining the election is
derived as follows
P((cid:92) chosen) =Probability political party X wins
X
1 1
= P(Z (cid:33)(cid:92)ˆ ,Z (cid:31)(cid:73)ˆ )(cid:14) P(Z (cid:33)(cid:92)ˆ ,Z (cid:33)(cid:73)ˆ )(cid:14) P(Z (cid:31)(cid:92)ˆ ,Z (cid:31)(cid:73)ˆ )
1 2 2 1 2 2 1 2
= P(Z (cid:33)(cid:92)ˆ ,Z (cid:31)(cid:73)ˆ )(cid:14)P(Z (cid:33)(cid:92)ˆ ,Z (cid:33)(cid:73)ˆ )
1 2 1 2
= P(Z (cid:33)(cid:92)ˆ )P(Z (cid:31)(cid:73)ˆ )(cid:14)P(Z (cid:33)(cid:92)ˆ )P(Z (cid:33)(cid:73)ˆ )
1 2 1 2
(cid:62) (cid:64)
= (1(cid:16)F((cid:92)ˆ ))F((cid:73)ˆ )(cid:14)(1(cid:16)F((cid:73)ˆ )
= (1(cid:16)F((cid:92)ˆ )). (7)
Note that the result shown in the second step derives from equation (6), whereas
the outcome shown in the third step arises because Z and Z are independent.
1 2
Similarly, P((cid:92) chosen)= Probability political party Y wins
Y
1 1
=P(Z (cid:33)(cid:73)ˆ ,Z (cid:31)(cid:92)ˆ )(cid:14) P(Z (cid:33)(cid:73)ˆ ,Z (cid:33)(cid:92)ˆ )(cid:14) P(Z (cid:31)(cid:73)ˆ ,Z (cid:31)(cid:92)ˆ )
2 1 2 2 1 2 2 1
= (1(cid:16)F((cid:73)ˆ )). (8)

12 As the political parties are making decisions in two dimensions, the political parties’ chances of
winning the election will be different from the case where the agents’ decision set is in one
dimension. Hence, we restructure the standard median voter model to accommodate the additional
dimensionality of the problem.
13 In such cases, the probability of winning for each political party is ½.

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